White House press secretary Sarah Sanders released a statement accusing Mr Acosta of "placing his hands on a young woman just trying to do her job as a White House intern," calling it "absolutely unacceptable".

The interaction between Mr Acosta and the intern was brief, and Mr Acosta appeared to brush her arm as she reached for the microphone and he tried to hold on to it. "Pardon me, ma'am," he told her.

Mr Acosta tweeted that Ms Sanders's statement that he put his hands on the aide was "a lie".

"I came in here as a nice person wanting to answer questions, and I had people jumping out of their seats screaming questions at me," said Mr Trump, who talked for nearly 90 minutes despite the run-ins with reporters.

"You should let me run the country," Mr Trump said. "You run CNN and if you did it well, your ratings would be much better."

"CNN should be ashamed of itself having you work for them," the president said to Mr Acosta. "You are a rude, terrible person. You shouldn't be working for CNN. The way you treat Sarah Sanders is horrible. The way you treat other people is horrible. You shouldn't treat people that way."

Mr Alexander came to his colleague's defence. "I've travelled with him and watched him," Mr Alexander said. "He's a diligent reporter who busts his butt like the rest of us."

'They are disturbingly un-American'

Mr Acosta stood back up and began mentioning, without a microphone, the explosive devices that were recently sent to CNN and some of the president's political opponents.

"Just sit down," Mr Trump said. "When you report fake news, which CNN does a lot, you are the enemy of the people."

After the exchange, CNN, through its public relations department's Twitter feed, said Mr Trump's attacks on the press have gone too far.

"They are not only dangerous, they are disturbingly un-American," CNN said.

"While President Trump has made it clear he does not respect a free press, he has a sworn obligation to protect it. A free press is vital to democracy, and we stand behind Jim Acosta and his fellow journalists everywhere."